See Where can Building Blocks be stored?

It is even worse than this! AutoText building blocks gets stored by default to your Normal Template and other Building Blocks are stored by default in your personal Building Blocks.dotx file.
Neither of these templates are suited for sharing.

Instead, you want to store your custom Building Blocks to be shared in either a shared document template or a shared Global Template. A document template if intended for use in only documents created from that template; a global template if intended for use in multiple documents.
Document templates should be stored in the Workgroup Templates folder; Global Templates would be stored in the user's Word Startup Folder.

The good news is that you can use the Building Blocks Organizer to move existing Building Blocks to a different template. To do this, the new template must have at least one building block stored in it.